Then consider the terms on the right hand side, firstly since we know that p must be odd p -1 and p + 1 must be even. so we have two of the factors we require.

Additionally since p – 1 and p + 1 effectively form 2 consecutive even numbers one of them must be a multiple of 4 thus we have another of our factors of 2. So far we have 2×2×2, now to get the factor of 3

p – 1, p & p + 1 form three consecutive numbers. in any three consecutive numbers one will be a multiple of 3, we know it is not p which is a multiple of 3, as this is prime, hence either p – 1 or p + 1 is a multiple. Therefore p2 – 1 has the factors 2, 2, 2 & 3 hence:

p^2 – 1 = 24n

Why must p be greater than 3? Because 3 is the only number which is both a multiple of 3 and prime.